Twenty faces rounding toward the sphere — form that flows and will not hold an edge.
The Form
The icosahedron is the most many-faced of the triangular solids, twenty equilateral triangles gathered five to a vertex around twelve points. Of all the Platonic solids it comes nearest to the sphere, its densely tiled surface rounding away the hard corners that mark the simpler forms. Roll it and it very nearly rolls; hold it and it fills the hand with a sense of smoothness and yield. Its abundance of faces gives it a fluid, almost liquid character, as though it were a drop of the ideal caught momentarily in facets.
The icosahedron is the dual of the dodecahedron, the two most complex solids paired as reciprocals in the way the cube and octahedron are paired. Where the dodecahedron gathers space into twelve broad pentagons, the icosahedron scatters it into twenty keen triangles, and each contains the other in the arithmetic of their vertices and faces. It is the last of the four elemental bodies, and the roundest, the one whose geometry most readily suggests flowing rather than standing.
Correspondences
| Attribute | Value |
|---|---|
| Faces | 20 |
| Face shape | Equilateral triangle |
| Edges | 30 |
| Vertices | 12 |
| Element | Water |
| Dual | Dodecahedron |
Meaning
Plato assigned the icosahedron to Water, and its rounded, flowing form makes the choice feel natural. Water is the element that takes the shape of its vessel, that moves and pools and yields, and the icosahedron, nearest of the solids to the fluid sphere, embodies that pliancy. In Alchemy Water is the solvent and the dissolver, the medium in which the fixed is loosened and made ready for change, the maternal element of gestation and flow. The icosahedron thus stands for adaptability, emotion, and the receptive current, the geometry of that which conforms without breaking. To contemplate it is to feel how the greatest complexity can arrive at the greatest smoothness.